1. Review Chapter 1-8 in Jackson
PHY 712 Electrodynamics
9-9:50 AM Olin 105
Plan for Lecture 20:
Review Chapter 1-8 in Jackson
Math identities and tricks
Maxwell’s equations
Examples and homework problems
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PHY 712 Spring Lecture 20

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PHY 712 Spring Lecture 20

3. Career advising event –
Events next week --
Career advising event –
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PHY 712 Spring Lecture 20

4. Review of mathematical relationships
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PHY 712 Spring Lecture 20

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6. Some properties of a delta function In one-dimension:
In three-dimensions:
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PHY 712 Spring Lecture 20

7. Orthogonal functions useful for angular representations
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PHY 712 Spring Lecture 20

8. Useful identities related to Coulomb kernel:
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PHY 712 Spring Lecture 20

9. Green’s theorem for electrostatics
volume integral over source
surface integrals incorporating boundary values
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PHY 712 Spring Lecture 20

10. Maxwell’s equations Review 03/01/2019
PHY 712 Spring Lecture 20

11. Maxwell’s equations Review -- continued 03/01/2019
PHY 712 Spring Lecture 20

12. Review -- continued
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PHY 712 Spring Lecture 20

13. Review -- continued
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PHY 712 Spring Lecture 20

14. Useful for spatially confined sources.
Review – continued – focusing on statics --
When to solve equations using integral form
versus differential form?
Examples from electrostatic and magnetostatic cases:
Useful for spatially confined sources.
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PHY 712 Spring Lecture 20

15. Review -- continued
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PHY 712 Spring Lecture 20

16. Example of use of spherical harmonic expansion:
Problem #4.9 in Jackson. A point charge q is located in free space a distance d from the center of a dielectric sphere of radius a (a<d) and dielectric constant e/e0. Find the electrostatic potential. a q d
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PHY 712 Spring Lecture 20

17. Review of HW -- continued
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PHY 712 Spring Lecture 20

18. a q d
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PHY 712 Spring Lecture 20

19. 2 equations and 2 unknowns for each l
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PHY 712 Spring Lecture 20

20. Hyperfine interaction energy:
Review -- continued
Hyperfine interaction energy:
Putting all of the terms together:
In this expression the brackets indicate evaluating the expectation value relative to the electronic state.
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PHY 712 Spring Lecture 20

21. Solution to problem using PHY 114 ideas
Comment on HW #8
Consider an infinitely long wire with radius a, oriented along the z axis. There is a steady uniform current inside the wire. Specifically the current is along the z-axis with the magnitude of J0 for ρ ≤ a and zero for ρ > a, where ρ denotes the radial parameter of the natural cylindrical coordinates of the system.
Find the vector potential (A) for all ρ.
Find the magnetic flux field (B) for all ρ.
Solution to problem using PHY 114 ideas
In this case, it is convenient to solve part b first.
Top view for r < a
Top view for r > a J0 B B
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PHY 712 Spring Lecture 20

22. Comment on HW #11 -- continued Top view for r < a B B
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PHY 712 Spring Lecture 20

23. Comment on HW #8 -- continuedJ0
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PHY 712 Spring Lecture 20

24. Comment on HW #9
A sphere of radius a carries a uniform surface charge distribution s. The sphere is rotated about a diameter with constant angular velocity w. Find the vector potential A and magnetic field B both inside and outside the sphere. w r
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PHY 712 Spring Lecture 20

25. Comment on HW #9 -- continued
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PHY 712 Spring Lecture 20

26. Reflectance for s-polarization
Correction to Lecture 18
Reflectance for s-polarization
Reflectance for p-polarization
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PHY 712 Spring Lecture 20

27. s-polarization p-polarization 03/01/2019
PHY 712 Spring Lecture 20